Method for spectrophotometric blood oxygenation monitoring

ABSTRACT

A method and apparatus for non-invasively determining the blood oxygenation within a subject&#39;s tissue is provided that utilizes a near infrared spectrophotometric (NIRS) sensor capable of transmitting a light signal into the tissue of a subject and sensing the light signal once it has passed through the tissue via transmittance or reflectance.

This application is a continuation of U.S. patent application Ser. No.11/376,894 filed Mar. 16, 2006, which is a continuation of U.S. Pat. No.7,072,701 filed Jul. 24, 2003, which claims the benefit of the filingdate of U.S. Provisional Applications 60/398,937, filed 26 Jul. 2002,and 60/407,277 filed 30 Aug. 2002.

This invention was made with Government support under Contract No.1R43NS045488-01 awarded by the Department of Health & Human Services.The Government has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Technical Field

This invention relates to methods for non-invasively determiningbiological tissue oxygenation in general, and to non-invasive methodsutilizing near-infrared spectroscopy (NIRS) techniques in particular.

2. Background Information

The molecule that carries the oxygen in the blood is hemoglobin.Oxygenated hemoglobin is called oxyhemoglobin (HbO₂) and deoxygenatedhemoglobin is deoxyhemoglobin (Hb). Total hemoglobin is the summation ofthe two states of hemoglobin (Total Hb=HbO₂+Hb), and is proportional torelative blood volume changes, provided that the hematocrit orhemoglobin concentration of the blood is unchanged. The mammaliancardiovascular system consists of a blood pumping mechanism (the heart),a blood transportation system (blood vessels), and a blood oxygenationsystem (the lungs). Blood oxygenated by the lungs passes through theheart and is pumped into the arterial vascular system. Under normalconditions, oxygenated arterial blood consists predominately of HbO₂.Large arterial blood vessels branch off into smaller branches calledarterioles, which profuse throughout biological tissue. The arteriolesbranch off into capillaries, the smallest blood vessels. In thecapillaries, oxygen carried by hemoglobin is transported to the cells inthe tissue, resulting in the release of oxygen molecules (HbO₂

Hb). Under normal conditions, only a fraction of the HbO₂ molecules giveup oxygen to the tissue, depending on the cellular metabolic need. Thecapillaries then combine together into venuoles, the beginning of thevenous circulatory system. Venuoles then combine into larger bloodvessels called veins. The veins further combine and return to the heart,and then venous blood is pumped to the lungs. In the lungs, deoxygenatedhemoglobin Hb collects oxygen becoming HbO₂ again and the circulatoryprocess is repeated.

Oxygen saturation is defined as:

$\begin{matrix}{{O_{2}\mspace{14mu}{saturation}\mspace{14mu}\%} = {\frac{{HbO}_{2}}{\left( {{HbO}_{2} + {Hb}} \right)}*100\%}} & \left( {{Eqn}.\mspace{14mu} 1} \right)\end{matrix}$In the arterial circulatory system under normal conditions, there is ahigh proportion of HbO₂ to Hb, resulting in an arterial oxygensaturation (defined as SaO₂%) of 95-100%. After delivery of oxygen totissue via the capillaries, the proportion of HbO₂ to Hb decreases.Therefore, the measured oxygen saturation of venous blood (defined asSvO₂%) is lower and may be about 70%.

One spectrophotometric method, called pulse oximetry, determinesarterial oxygen saturation (SaO₂) of peripheral tissue (i.e., finger,ear, nose) by monitoring pulsatile optical attenuation changes ofdetected light induced by pulsatile arterial blood volume changes in thearteriolar vascular system. The method of pulse oximetry requirespulsatile blood volume changes in order to make a measurement. Sincevenous blood is not pulsatile, pulse oximetry cannot provide anyinformation about venous blood.

Near-infrared spectroscopy (NIRS) is an optical spectrophotometricmethod of continually monitoring tissue oxygenation that does notrequire pulsatile blood volume to calculate parameters of clinicalvalue. The NIRS method is based on the principle that light in thenear-infrared range (700 to 1,000 nm) can pass easily through skin, boneand other tissues where it encounters hemoglobin located mainly withinmicro-circulation passages (e.g., capillaries, arterioles, andvenuoles). Hemoglobin exposed to light in the near infra-red range hasspecific absorption spectra that varies depending on its oxidation state(i.e., oxyhemoglobin (HbO₂) and deoxyhemoglobin (Hb) each act as adistinct chromophore). By using light sources that transmitnear-infrared light at specific different wavelengths, and measuringchanges in transmitted or reflected light attenuation, concentrationchanges of the oxyhemoglobin (HbO₂) and deoxyhemoglobin (Hb) can bemonitored. The ability to continually monitor cerebral oxygenationlevels is particularly valuable for those patients subject to acondition in which oxygenation levels in the brain may be compromised,leading to brain damage or death.

The apparatus used in NIRS analysis typically includes a plurality oflight sources, one or more light detectors for detecting reflected ortransmitted light, and a processor for processing signals that representthe light emanating from the light source and the light detected by thelight detector. Light sources such as light emitting diodes (LEDs) orlaser diodes that produce light emissions in the wavelength range of700-1000 nm at an intensity below that which would damage the biologicaltissue being examined are typically used. A photodiode or other lightsource detector is used to detect light reflected from or passed throughthe tissue being examined. The processor takes the signals from thelight sources and the light detector and analyzes those signals in termsof their intensity and wave properties.

It is known that relative changes of the concentrations of HbO₂ and Hbcan be evaluated using apparatus similar to that described above,including a processor programmed to utilize a variant of theBeer-Lambert Law, which accounts for optical attenuation in a highlyscattering medium like biological tissue. The modified Beer-Lambert Lawcan be expressed as:A _(λ)=−log(I/I ₀)_(λ)=α_(λ) *C*d*B _(λ) +G  (Eqn. 2)wherein “A_(λ)” represents the optical attenuation in tissue at aparticular wavelength λ (units: optical density or OD); “I_(o)”represents the incident light intensity (units: W/cm²); “I” representsthe detected light intensity; “α_(λ)” represents the wavelengthdependent absorption coefficient of the chromophore (units:OD*cm⁻*μM⁻¹); “C” represents the concentration of chromophore (units:μM); “d” represents the light source to detector (optode) separationdistance (units: cm); “B_(λ)” represents the wavelength dependent lightscattering differential pathlength factor (unitless); and “G” representslight attenuation due to scattering within tissue (units: OD). Theproduct of “d*B_(λ)” represents the effective pathlength of photontraveling through the tissue.

Absolute measurement of chromophore concentration (C) is very difficultbecause G is unknown or difficult to ascertain. However, over areasonable measuring period of several hours to days, G can beconsidered to remain constant, thereby allowing for the measurement ofrelative changes of chromophore from a zero reference baseline. Thus, iftime t₁ marks the start of an optical measurement (i.e., a base line)and time t₂ is an arbitrary point in time after t₁, a change inattenuation (ΔA) between t₁ and t₂ can be calculated, and variables Gand 1_(o) will cancel out providing that they remain constant.

The change in chromophore concentration (ΔC=C(t₂)−C(t₁)) can bedetermined from the change in attenuation AA, for example using thefollowing equation derived from the modified Beer-Lambert Law:ΔA _(λ)=−log(I _(t2) /I _(t1))_(λ)=α_(λ) *ΔC*d*B _(λ)  (Eqn. 3)Presently known MRS algorithms that are designed to calculate therelative change in concentration of more than one chromophore use amultivariate form of Equation 2 or 3. To distinguish between, and tocompute relative concentration changes in, oxyhemoglobin (ΔHbO₂) anddeoxyhemoglobin (ΔHb), a minimum of two different wavelengths aretypically used. The concentration of the HbO₂ and Hb within the examinedtissue is determined in μmoles per liter of tissue (μM).

The above-described MRS approach to determine oxygenation levels isuseful, but it is limited in that it only provides information regardinga change in the level of oxygenation within the tissue. It does notprovide a means for determining the absolute value of oxygen saturationwithin the biological tissue.

At present, information regarding the relative contributions of venousand arterial blood within tissue examined by NIRS is either arbitrarilychosen or is determined by invasive sampling of the blood as a processindependent from the NIRS examination. For example, it has beenestimated that NIRS examined brain tissue comprising about 60 to 80%venous blood and about 20 to 40% arterial blood. Blood samples fromcatheters placed in venous drainage sites such as the internal jugularvein, jugular bulb, or sagittal sinus have been used to evaluate NIRSmeasurements. Results from animal studies have shown that NIRSinterrogated tissue consists of a mixed vascular bed with avenous-to-arterial ratio of about 2:1 as determined from multiple linearregression analysis of sagittal sinus oxygen saturation (SssO₂) andarterial oxygen saturation (SaO₂). An expression representing the mixedvenous/arterial oxygen saturation (SmvO₂) in MRS examined tissue isshown by the equation:SmvO ₂ =Kv*SvO ₂ +Ka*SaO ₂  (Eqn. 4)where “SvO₂” represents venous oxygen saturation; “SaO₂” representsarterial oxygen saturation; and Kv and Ka are the weighted venous andarterial contributions respectively, with Kv+Ka=1. The parameters Kv andKa may have constant values, or they may be a function of SvO₂ and SaO₂.Determined oxygen saturation from the internal jugular vein (SijvO₂),jugular bulb (SjbO₂), or sagittal sinus (SssO₂) can be used to representSvO₂. Therefore, the value of each term in Equation 4 is empiricallydetermined, typically by discretely sampling or continuously monitoringand subsequently evaluating patient arterial and venous blood fromtissue that the NIRS sensor is examining, and using regression analysisto determine the relative contributions of venous and arterial bloodindependent of the NIRS examination.

To non-invasively determine oxygen saturation within tissue at certaindepth, it is necessary to limit the influence from the superficialtissues. For example, to determine brain oxygen saturation of adulthuman with NIRS technology, the contamination from extracraninal tissue(scalp and skull) must be eliminated or limited.

What is needed, therefore, is a method for non-invasively determiningthe level of oxygen saturation within biological tissue that candetermine the absolute oxygen saturation value rather than a change inlevel; a method that provides calibration means to account for energylosses (i.e., light attenuation) due to light scattering within tissue,other background absorption losses from biological compounds, and otherunknown losses including measuring apparatus variability; and a methodthat can non-invasively determine oxygen saturation within tissue atcertain depth by limiting the influence from the superficial tissues.

DISCLOSURE OF THE INVENTION

It is, therefore, an object of the present invention to provide a methodfor non-invasively determining the absolute oxygen saturation valuewithin biological tissue.

It is a further object of the present invention to provide a method thatprovides calibration means to account for energy losses due toscattering as well as other background absorption from biologicalcompounds.

It is a still further object of the present invention to provide amethod that can non-invasively determine oxygen saturation within tissueat certain depth that limits the influence from the superficial tissues.

According to the present invention, a method and apparatus fornon-invasively determining the blood oxygen saturation level within asubject's tissue is provided that utilizes a near infraredspectrophotometric (NIRS) sensor capable of transmitting a light signalinto the tissue of a subject and sensing the light signal once it haspassed through the tissue via transmittance or reflectance. The methodincludes the steps of: (1) transmitting a light signal into thesubject's tissue, wherein the transmitted light signal includes a firstwavelength, a second wavelength, and a third wavelength; (2) sensing afirst intensity and a second intensity of the light signal, along thefirst, second, and third wavelengths after the light signal travelsthrough the subject at a first and second predetermined distance; (3)determining an attenuation of the light signal for each of the first,second, and third wavelengths using the sensed first intensity andsensed second intensity of the first, second, and third wavelengths; (4)determining a difference in attenuation of the light signal between thefirst wavelength and the second wavelength, and between the firstwavelength and the third wavelength; and (5) determining the bloodoxygen saturation level within the subject's tissue using the differencein attenuation between the first wavelength and the second wavelength,and the difference in attenuation between the first wavelength and thethird wavelength.

The present method makes it possible to account for energy losses (i.e.,light attenuation) due to light scattering within tissue, otherbackground absorption losses from biological compounds, and otherunknown losses including measuring apparatus variability. By determiningdifferential attenuation as a function of wavelength, the energy lossesdue to scattering as well as other background absorption from biologicalcompounds are cancelled out or minimized relative to the attenuationattributable to deoxyhemoglobin, and attenuation attributable tooxyhemoglobin.

In order to account for the resulting minimized differential attenuationattributable to tissue light scattering characteristics, fixed lightabsorbing components, and measuring apparatus characteristics, each ofthe parameters must be measured or calibrated out. Since directmeasurement is difficult, calibration to empirically determined datacombined with data developed using the NIRS sensor is performed by usingregression techniques. The empirically determined data is collected ator about the same time the data is developed with the NIRS sensor. Oncethe calibration parameters associated with attenuation attributable totissue light scattering characteristics, fixed light absorbingcomponents, and measuring apparatus characteristics have beendetermined, the NIRS sensor can be calibrated.

The calibrated sensor can then be used to accurately and non-invasivelydetermine the total oxygen saturation level in the original subjecttissue or other subject tissue. In addition, if the effective pathlengthof photon traveling through the tissue is known, for example, theseparation distance (“d”) between the light source to the light detectoris known or is determinable, and the value of “B_(λ)”, which representsthe wavelength dependent light scattering differential pathlength factoris known or is determinable, then the total amount of concentrations ofdeoxyhemoglobin (Hb) and oxyhemoglobin (HbO₂) within the examined tissuecan be determined using the present method and apparatus.

The calibrated sensor can be used subsequently to calibrate similarsensors without having to invasively produce a blood sample. Hence, thepresent method and apparatus enables a non-invasive determination of theblood oxygen saturation level within tissue. For example, an operatorcan create reference values by sensing a light signal or other referencemedium using the calibrated sensor. The operator can then calibrate anuncalibrated sensor by sensing the same light signal or referencemedium, and subsequently adjusting the uncalibrated sensor intoagreement with the calibrated sensor. Hence, once a reference sensor iscreated, other similar sensors can be calibrated without the need forinvasive procedure.

There are, therefore, several advantages provided by the present methodand apparatus. Those advantages include: 1) a practical non-invasivemethod and apparatus for determining oxygen saturation within tissuethat can be used to determine the total blood oxygen saturation withintissue as opposed to a change in blood oxygen saturation; 2) acalibration method that accounts for energy losses (e.g., lightattenuation) due to light scattering within tissue, other backgroundabsorption losses from biological compounds, and other unknown lossesincluding measuring apparatus variability; 3) a practical non-invasivemethod and apparatus for determining oxygen saturation within tissuethat can distinguish between the contribution of oxygen saturationattributable to venous blood and that saturation attributable toarterial blood; and 4) a practical non-invasive method and apparatus fordetermining oxygen saturation within tissue at certain depth that limitsthe influence from the superficial tissues.

In an alternative embodiment, aspects of the above-described methodologyare combined with pulse oximetry techniques to provide a non-invasivemethod of distinguishing between blood oxygen saturation within tissuethat is attributable to venous blood and that which is attributable toarterial blood. Pulse oximetry is used to determine arterial oxygensaturation, and the arterial oxygen saturation is, in turn, used todetermine the venous oxygen saturation.

These and other objects, features, and advantages of the presentinvention method and apparatus will become apparent in light of thedetailed description of the invention provided below and theaccompanying drawings. The methodology and apparatus described belowconstitute a preferred embodiment of the underlying invention and donot, therefore, constitute all aspects of the invention that will or maybecome apparent by one of skill in the art after consideration of theinvention disclosed overall herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic representation of a NIRS sensor.

FIG. 2 is a diagrammatic representation of a NIRS sensor placed on asubject's head.

FIG. 3 is a diagrammatic view of a NIRS sensor.

FIG. 4 is a block diagram of the present methodology for calibrating aMRS sensor.

FIG. 5 is a graph showing an exemplary plot of absorption coefficientvs. wavelength.

DETAILED DESCRIPTION THE INVENTION

The present method of and apparatus for non-invasively determining theblood oxygen saturation level within a subject's tissue is provided thatutilizes a near infrared spectrophotometric (NIRS) sensor that includesa transducer capable of transmitting a light signal into the tissue of asubject and sensing the light signal once it has passed through thetissue via transmittance or reflectance. The present method andapparatus can be used with a variety of NIRS sensors. The present methodis not limited to use with this preferred NIRS sensor, however.

Referring to FIGS. 1-5, the preferred NIRS sensor includes a transducerportion 10 and processor portion 12. The transducer portion 10 includesan assembly housing 14 and a connector housing 16. The assembly housing14, which is a flexible structure that can be attached directly to asubject's body, includes one or more light sources 18 and lightdetectors 19, 20. A disposable adhesive envelope or pad is used formounting the assembly housing 14 easily and securely to the subject'sskin. Light signals of known but different wavelengths from the lightsources 18 emit through a prism assembly. The light sources 18 arepreferably laser diodes that emit light at a narrow spectral bandwidthat predetermined wavelengths. In one embodiment, the laser diodes aremounted within the connector housing 16. The laser diodes are opticallyinterfaced with a fiber optic light guide to the prism assembly that isdisposed within the assembly housing 14. In a second embodiment, thelight sources 18 are mounted within the assembly housing 14. A firstconnector cable 26 connects the assembly housing 14 to the connectorhousing 16 and a second connector cable 28 connects the connectorhousing 16 to the processor portion 12. The light detector 20 includesone or more photodiodes. The photodiodes are also operably connected tothe processor portion 12 via the first and second connector cables 26,28. The processor portion 12 includes a processor for processing lightintensity signals from the light sources 18 and the light detectors 19,20.

The processor utilizes an algorithm that characterizes a change inattenuation as a function of the difference in attenuation betweendifferent wavelengths. The present method advantageously accounts forbut minimizes the effects of pathlength and parameter “E”, whichrepresents energy losses (i.e., light attenuation) due to lightscattering within tissue (G), other background absorption losses frombiological compounds (F), and other unknown losses including measuringapparatus variability (N).E=G+F+N.

Referring to FIG. 1, the absorption A_(bλ) detected from the deep lightdetector 20 comprises attenuation and energy loss from both the deep andshallow tissue, while the absorption A_(xλ) detected from the shallowlight detector 19 comprises attenuation and energy loss from shallowtissue only. Absorptions A_(bλ) and A_(xλ) can be expressed in the formof Equation 5 and Equation 6 below which is a modified version ofEquation 2 that accounts for energy losses due to “E”:A _(bλ)=−log(I _(b) /I _(o))_(λ)=α_(λ) *C _(b) *L _(b)+α_(λ) *C _(x) *L_(x) +E _(λ)  (Eqn. 5)A _(xλ)=−log(I _(x) /I _(o))_(λ)=α_(λ) *C _(x) *L _(x) +E _(xλ)  (Eqn.6)Substituting Equation 6, into Equation 5 yields which representsattenuation and energy loss from deep tissue only:

$\begin{matrix}{A_{\lambda}^{\prime} = {{A_{b\;\lambda} - A_{x\;\lambda}} = {{{\alpha_{\lambda}*C_{b}*L_{b}} + \left( {E_{\lambda} - E_{x\;\lambda}} \right)} = {- {\log\left( \frac{I_{b}}{I_{x}} \right)}_{\lambda}}}}} & \left( {{Eqn}.\mspace{14mu} 7} \right)\end{matrix}$Where L is the effective pathlength of the photon traveling through thedeep tissue and A′₁ and A′₂ are the absorptions of two differentwavelengths. Let E′_(λ)=E_(λ)−E_(xλ), therefore:A′ ₁ −A′ ₂ =ΔA′ ₁₂  (Eqn. 8)Substituting Equation 7 into Equation 8 for A′₁ and A′₂, αA′₁₂ can beexpressed as:ΔA′ ₁₂=α_(λ12) *C _(b) *L _(b) +ΔE′ ₁₂  (Eqn. 9)and rewritten Equation 9 in expanded form:

$\begin{matrix}{{\Delta\; A_{12}^{\prime}} = {{{\left\langle {{\left( {\alpha_{r\; 1} - \alpha_{r\; 2}} \right)\lbrack{Hb}\rbrack}_{b} + {\left( {\alpha_{o\; 1} - \alpha_{o\; 2}} \right)\left\lbrack {HbO}_{2} \right\rbrack}_{b}} \right\rangle L_{b}} + \left( {E_{1}^{\prime} - E_{2}^{\prime}} \right)} = {\left( {{\Delta\alpha}_{r\; 12}*\lbrack{Hb}\rbrack_{b}*L_{b}} \right) + \left( {{\Delta\alpha}_{o\; 12}*\left\lbrack {HbO}_{2} \right\rbrack_{b}*L_{b}} \right) + {\Delta\; E_{12}^{\prime}}}}} & \left( {{Eqn}.\mspace{14mu} 10} \right)\end{matrix}$where:

(Δα_(r12)*[Hb]_(b)*L_(b)) represents the attenuation attributable to Hb;

(Δα_(o12)*[HbO₂]_(b)*L_(b)) represents the attenuation attributable toHbO₂; and

ΔE′₁₂ represents energy losses (i.e. light attenuation) due to lightscattering within tissue, other background absorption losses frombiological compounds, and other unknown losses including measuringapparatus variability.

The multivariate form of Equation 10 is used to determine [HbO₂]_(b) and[Hb]_(b) with three different wavelengths:

$\begin{matrix}{{\left\lfloor \begin{matrix}{{\Delta\; A_{12}^{\prime}} - {\Delta\; E_{12}^{\prime}}} \\{{\Delta\; A_{13}^{\prime}} - {\Delta\; E_{13}^{\prime}}}\end{matrix} \right\rfloor\left( L_{b} \right)^{- 1}} = {\left\lfloor \begin{matrix}{\Delta\alpha}_{r\; 12} & {\Delta\alpha}_{o\; 12} \\{\Delta\alpha}_{r\; 13} & {\Delta\alpha}_{o\; 13}\end{matrix} \right\rfloor\left\lfloor \begin{matrix}\lbrack{Hb}\rbrack_{b} \\\left\lbrack {HbO}_{2} \right\rbrack_{b}\end{matrix} \right\rfloor}} & \left( {{Eqn}.\mspace{14mu} 11} \right)\end{matrix}$Rearranging and solving for [HbO₂]_(b) and [Hb]_(b), simplifying the Δαmatrix into [Δα′]:

$\begin{matrix}{{{{\begin{bmatrix}{\Delta\; A_{12}^{\prime}} \\{\Delta\; A_{13}^{\prime}}\end{bmatrix}\left\lbrack {\Delta\alpha}^{\prime} \right\rbrack}^{- 1}\left( L_{b} \right)^{- 1}} - {{\begin{bmatrix}{\Delta\; E_{12}^{\prime}} \\{\Delta\; E_{13}^{\prime}}\end{bmatrix}\left\lbrack {\Delta\alpha}^{\prime} \right\rbrack}^{- 1}\left( L_{b} \right)^{- 1}}} = \begin{bmatrix}\lbrack{Hb}\rbrack_{b} \\\left\lbrack {HbO}_{2} \right\rbrack_{b}\end{bmatrix}} & \left( {{Eqn}.\mspace{14mu} 12} \right)\end{matrix}$Then combined matrices [ΔA′] [Δα′]⁻¹=[A_(C)] and [ΔE] [Δα′]⁻¹=[Ψ_(c)]:

$\begin{matrix}{{{\begin{bmatrix}A_{Hb} \\A_{{HbO}_{2}}\end{bmatrix}\left( L_{b} \right)^{- 1}} - {\begin{bmatrix}\Psi_{Hb} \\\Psi_{{HbO}_{2}}\end{bmatrix}\left( L_{b} \right)^{- 1}}} = \begin{bmatrix}\lbrack{Hb}\rbrack_{b} \\\left\lbrack {HbO}_{2} \right\rbrack_{b}\end{bmatrix}} & \left( {{Eqn}.\mspace{14mu} 13} \right)\end{matrix}$The parameters A_(HB) and A_(HbO2) represent the product of the matrices[ΔA_(λ)] and [Δa′]⁻¹ and the parameters Ψ_(Hb) and Ψ_(HbO2) representthe product of the matrices [ΔE′_(λ)] and [Δα′]⁻¹. To determine thelevel of cerebral blood oxygen saturation (SnO₂), Equation 13 isrearranged using the form of Equation 1 and is expressed as follows:

$\begin{matrix}{{{SnO}_{2}\mspace{14mu}\%} = {\frac{\left( {A_{{HbO}_{2}} - \Psi_{{HbO}_{2}}} \right)}{\left( {A_{{HbO}_{2}} - \Psi_{{HbO}_{2}} + A_{Hb} - \Psi_{Hb}} \right)}*100\%}} & \left( {{Eqn}.\mspace{14mu} 14} \right)\end{matrix}$Note that the effective pathlength L_(b) cancels out in the manipulationfrom Equation 13 to Equation 14.

The value for SnO₂ is initially determined from SmvO₂ using Equation 4and the empirically determined values for SvO₂ and SaO₂. The empiricallydetermined values for SvO₂ and SaO₂ are based on data developed bydiscrete sampling or continuous monitoring of the subject's bloodperformed at or about the same time as the sensing of the tissue withthe sensor. The temporal and physical proximity of the NIRS sensing andthe development of the empirical data helps assure accuracy. The initialvalues for Kv and Ka within Equation 4 are clinically reasonable valuesfor the circumstances at hand. The values for A_(HbO2) and A_(Hb) aredetermined mathematically using the values for I_(bλ) and I_(xλ) foreach wavelength sensed with the MRS sensor (e.g., using Equation 5 and6). The calibration parameters Ψ_(Hb) and Ψ_(HbO2), which account forenergy losses due to scattering as well as other background absorptionfrom biological compounds, are then determined using Equation 14 andnon-linear regression techniques by correlation to different weightedvalues of SvO₂ and SaO₂ (i.e., different values of Ka and Kv).Statistically acceptable values of Kv and Ka and Ψ_(Hb) and Ψ_(HbO2) areconverged upon using the non-linear regression techniques. Experimentalfindings show that after proper selection of Ka and Kv, the calibrationparameters Ψ_(Hb) and Ψ_(HbO2) are constant within a statisticallyacceptable margin of error for an individual NIRS sensor used to monitorbrain oxygenation on different human subjects. In other words, once thesensor is calibrated it can be used on various human subjects andproduce accurate information for each human subject. The same is truefor animal subjects.

In an alternative method of determining the absolute oxygen saturationvalue Equation 7 is rewritten:

$\begin{matrix}{{A_{\lambda}^{\prime} - E_{\lambda}^{\prime}} = {{{- {\log\left( \frac{I_{b}}{I_{x}} \right)}_{\lambda}} - E_{\lambda}^{\prime}} = {{\alpha_{\lambda}*C*L_{b}} = {\left( {{\alpha_{r\;\lambda}\lbrack{Hb}\rbrack}_{b} + {\alpha_{o\;\lambda}\left\lbrack {HbO}_{2} \right\rbrack}_{b}} \right)L_{b}}}}} & \left( {{Eqn}.\mspace{14mu} 15} \right)\end{matrix}$For a two wavelength system, let “R” be a calibration index parameter:

$\begin{matrix}{R = {\frac{A_{1}^{\prime} - E_{1}^{\prime}}{A_{2}^{\prime} - E_{2}^{\prime}} = {\frac{\left( {{\alpha_{r\; 1}\lbrack{Hb}\rbrack}_{b} + {\alpha_{o\; 1}\left\lbrack {HbO}_{2} \right\rbrack}_{b}} \right)L_{b}}{\left( {{\alpha_{r\; 2}\lbrack{Hb}\rbrack}_{b} + {\alpha_{o\; 2}\left\lbrack {HbO}_{2} \right\rbrack}_{b}} \right)L_{b}} = {\frac{\alpha_{r\; 1} + {\alpha_{o\; 1}\frac{\left\lbrack {HbO}_{2} \right\rbrack_{b}}{\lbrack{Hb}\rbrack_{b}}}}{\alpha_{r\; 2} + {\alpha_{o\; 2}\frac{\left\lbrack {HbO}_{2} \right\rbrack_{b}}{\lbrack{Hb}\rbrack_{b}}}} = \frac{\alpha_{r\; 1} + {\alpha_{o\; 1}\frac{{SnO}_{2}}{1 - {SnO}_{2}}}}{\alpha_{r\; 2} + {\alpha_{o\; 2}\frac{{SnO}_{2}}{1 - {SnO}_{2}}}}}}}} & \left( {{Eqn}.\mspace{14mu} 16} \right)\end{matrix}$Canceling out L_(b) and substituting:

$\frac{\left\lbrack {HbO}_{2} \right\rbrack_{b}}{\lbrack{Hb}\rbrack_{b}} = {{\frac{{SnO}_{2}}{1 - {SnO}_{2}}\mspace{14mu}{from}\mspace{14mu}{SnO}_{2}} = \frac{\left\lbrack {HbO}_{2} \right\rbrack_{b}}{\left\lbrack {HbO}_{2} \right\rbrack_{b} + \lbrack{Hb}\rbrack_{b}}}$the following expression for SnO₂ is obtained:

$\begin{matrix}{{SnO}_{2} = \frac{\alpha_{r\; 1} - {\alpha_{r\; 2}R}}{\left( {\alpha_{r\; 1} - \alpha_{o\; 1}} \right) + {\left( {\alpha_{o\; 2} - \alpha_{r\; 2}} \right)R}}} & \left( {{Eqn}.\mspace{14mu} 17} \right)\end{matrix}$

The value of A₁′ and A₂′ are determined by measuring I_(b) and I_(x) foreach wavelength. The parameters E′₁ and E′₂ can be considered asempirically determined calibration coefficients derived from the“best-fit” combinations of the weighted ratios of venous and arterialblood-oxygen saturation of the brain. By using non-linear regressiontechniques, the values of E′₁ and E′₂ are determined by correlating todifferent combinations of venous and arterial oxygen saturation weightedvalues to find the “best-fit” relationship of “R” as a function of A₁′,A₂′, E′₁ and E′₂ (Equation 17) to a specific ratio of venous andarterial saturation weighted values.

In the determination of the SnO₂ percentage, the effective photonpathlength L_(b) cancels out. If, however, the photon pathlength isknown or estimated, then the determination of the total value of Hband/or HbO₂ is possible. For example, if a value for pathlength L_(b) isinput into Equation 13 along with the calibration values Ψ_(Hb) andΨ_(HbO2), then the total value of Hb and/or HbO₂ can be calculated.According to Equation 2, pathlength L can be estimated from the productof “B*d”. The light source to detector separation (optode) distanceparameter “d” in the pathlength calculation is a measurable value andcan be made constant by setting a fixed distance between light source todetector in the NIRS sensor design. Alternatively, the parameter “d” canbe measured once the optodes are placed on the subject by use ofcalipers, ruler, or other distance measurement means. The pathlengthdifferential factor “B” is more difficult to measure and requires moresophisticated equipment. From a large data set of measured neonatal andadult head differential pathlength factor values, an estimation of thevalue of “B” can be determined within a statistically acceptable marginof error. Substitution of these predetermined values of “B” intoEquation 13 results in the determination of the total values of Hb andHbO₂.

An alternative method of determining total values of Hb and HbO₂combines Equation 3 and Equation 13 together. The multivariate form ofEquation 3 is shown below:

$\begin{matrix}{\begin{bmatrix}{{- {\log\left( {I_{t\; 2}/I_{t\; 1}} \right)}_{\lambda\; 1}}/L_{\lambda\; 1}} \\{{- {\log\left( {I_{t\; 2}/I_{t\; 1}} \right)}_{\lambda\; 2}}/L_{\lambda\; 2}} \\{{- {\log\left( {I_{t\; 2}/I_{t\; 1}} \right)}_{\lambda\; 3}}/L_{\lambda\; 3}}\end{bmatrix} = {\left\lfloor \begin{matrix}\alpha_{{{Hb}\;{\lambda 1}}\;} & \alpha_{{{Hb}\; O_{2}{\lambda 1}}\;} \\\alpha_{{{Hb}\;{\lambda 2}}\;} & \alpha_{{{Hb}\; O_{2}{\lambda 2}}\;} \\\alpha_{{{Hb}\;{\lambda 3}}\;} & \alpha_{{{Hb}\; O_{2}{\lambda 3}}\;}\end{matrix} \right\rfloor*\begin{bmatrix}{\Delta\;{Hb}} \\{\Delta\;{HbO}_{2}}\end{bmatrix}}} & \left( {{Eqn}.\mspace{14mu} 18} \right)\end{matrix}$At time t=t₁, the values of ΔHb and ΔHbO₂ are zero. Applying Equation13, and knowing the calibration values of Ψ_(Hb) and Ψ_(HbO2) at apredetermined differential pathlength factor “B” and optode separation“d”, the total absolute values of Hb and HbO₂ are determined at timet=t₁, which are represented by [Hb]_(t1) and [HbO₂]_(t1) respectively.At time t=t₂, the values of ΔHb and ΔHbO₂ are then determined usingEquation 18. The total values of Hb and HbO₂ are then determined at timet=t₂ using the following equations:[Hb] _(t) ₂ ΔHb(t ₂)+[Hb] _(t) ₁   (Eqn. 19)[HbO ₂]_(t) ₂ =ΔHbO ₂(t ₂)[HbO ₂]_(t) ₁   (Eqn. 20)Equations 19 and 20 are valid only if all the shared parameters inEquations 13 and 18 are exact. Reduced to practice, the advantage ofcombining Equations 13 and 18 results in improved signal to noise ratio(SNR) in the calculation of the total values for Hb and HbO₂.Conversely, improved SNR in the calculation of SnO₂ is also obtainedfrom the following expression:

$\begin{matrix}{{{SnO}_{2}\mspace{14mu}\%} = {\frac{{HbO}_{2}}{\left( {{HbO}_{2} + {Hb}} \right)}*100\%}} & \left( {{Eqn}.\mspace{14mu} 21} \right)\end{matrix}$

After the calibration parameters Ψ_(Hb) and Ψ_(HbO2) are determinedusing the above-described methodology for an individual NIRS sensor,this particular sensor is said to be calibrated. A calibrated NIRSsensor affords accurate measurement of total tissue oxygen saturation,SnO₂, by non-invasive means. The calibrated sensor can be usedthereafter on any human patient, including adults and neonates. The sameis true for animal subject if the sensor was calibrated on animals.Although the present method is described above in terms of sensing bloodoxygenation within cerebral tissue, the present method and apparatus arenot limited to cerebral applications and can be used to determine bloodoxygenation within tissue found elsewhere within the subject's body.

According to an additional aspect of the present invention, theabove-described method can also be used to establish a calibrated“reference” sensor that can be used to calibrate similar sensors throughthe use of a phantom sample (also referred to as a “reference sample”).The phantom sample has optical characteristics that are similar to thetissue being examined by the MRS sensor. The calibrated reference MRSsensor is used to sense the phantom sample and produce reference values.Similar, but uncalibrated, NIRS sensors can thereafter be calibrated bysensing the same phantom sample and adjusting either the hardware of theuncalibrated sensor or the output of the uncalibrated sensor until theoutput of the uncalibrated sensor agrees with the reference valuesproduced by the calibrated reference sensor. Therefore, the calibrationparameters Ψ_(Hb) and Ψ_(HbO2) for the uncalibrated sensor would bedetermined from the phantom sample. This technique makes it unnecessaryto calibrate each new sensor in the manner described above, and therebyprovides a relatively quick and cost effective way to calibrate NIRSsensors.

Besides Hb and HbO₂, other biological constituents of interest (e.g.,cytochrome aa₃, etc.) could be determined using the multivariate formsof equations 2, 3, 6 or 7. For each additional constituent to bedetermined, an additional measuring wavelength will be needed.

In an alternative embodiment, the above-described methodology can becombined with pulse oximetry techniques to provide an alternativenon-invasive method of distinguishing between oxygen saturationattributable to venous blood and that attributable to arterial blood. Asdemonstrated by Equation 4, SmvO₂ is determined by the ratio of venousoxygen saturation SvO₂ and arterial oxygen saturation SaO₂. A calibratedNIRS sensor affords accurate measurement of total tissue oxygensaturation, SnO₂, by using regression techniques by correlation to mixedvenous oxygen saturation SmvO₂. Therefore, the following expression willresult:SnO ₂ =SmvO ₂ =K _(v) *SvO ₂ +Ka*SaO ₂  (Eqn. 22)Non-invasive pulse oximetry techniques can be used to determine thearterial oxygen saturation (SaO₂) of peripheral tissue (i.e., finger,ear, nose) by monitoring pulsatile optical attenuation changes ofdetected light induced by pulsatile arterial blood volume changes in thearteriolar vascular system. Arterial blood oxygen saturation determinedby pulse oximetry is clinically denoted as SpO₂. If NIRS monitoring andpulse oximetry monitoring are done simultaneously and SpO₂ is set equalto SaO₂ in Equation 23, then venous oxygen saturation can be determinedfrom the following expression:

$\begin{matrix}{{SvO}_{2} = \frac{{SnO}_{2} - \left( {{Ka}*{SpO}_{2}} \right)}{Kv}} & \left( {{Eqn}.\mspace{14mu} 23} \right)\end{matrix}$For the brain, venous oxygen saturation SvO₂ would be determined frominternal jugular vein (SijvO₂), jugular bulb (SjbO₂), or sagittal sinus(SssO₂) and the parameters Ka and Kv would be empirically determinedduring the calibration of the NIRS sensor. Under most physiologicalconditions, SpO₂ is representative of brain arterial oxygen saturationSaO₂. Therefore, depending on which venous saturation parameter was usedto calibrate the NIRS sensor, this clinically important parameter (i.e.,SijvO₂, SjbO₂, or SssO₂) can be determined by Equation 24 bynon-invasive means.

Since many changes and variations of the disclosed embodiment of theinvention may be made without departing from the inventive concept, itis not intended to limit the invention otherwise than as required by theappended claims.

What is claimed is:
 1. A method for non-invasively determining an absolute non-pulsatile blood oxygen saturation level within a subject's tissue, said method comprising the steps of: providing a sensor having at least one transducer in communication with a processor, the transducer having at least one light source, a first light detector spaced apart from the light source by a first distance, and a second light detector spaced apart from the light source by a second distance, wherein the first distance is less than the second distance; transmitting light signals from the light source into the subject's tissue, wherein the transmitted light signals include a plurality of wavelengths; sensing the light signals using the first light detector and the second light detector, and communicating information representative of the sensed light signals to the processor; determining an attenuation of the transmitted light signals for each of the plurality of wavelengths using the processor to process the information representative of the sensed light signals; and determining the absolute non-pulsatile blood oxygen saturation level within the subject's tissue using the processor, which determining includes determining a difference in attenuation between the plurality of wavelengths.
 2. The method of claim 1, further comprising the step of calibrating the sensor to account for energy losses attributable to one or more of light scattering, absorption from biological compounds other than hemoglobin, and apparatus variability.
 3. The method of claim 2, wherein the calibrating includes using information representative of a comparison of non-invasively collected oxygen saturation data and invasively collected oxygen saturation data.
 4. The method of claim 2, wherein the step of calibrating includes calibrating the sensor to be subject independent.
 5. The method of claim 1, further comprising the step of determining one or both of an absolute non-pulsatile oxyhemoglobin concentration value and an absolute non-pulsatile deoxyhemoglobin concentration value.
 6. The method of claim 1, further comprising the step of determining an arterial oxygen saturation of the subject using a pulse oximeter.
 7. The method of claim 6, further comprising the step of determining a venous oxygen saturation within the subject's tissue using the arterial oxygen saturation determined using the pulse oximeter.
 8. The method of claim 1, wherein the at least one transducer includes a first transducer and a second transducer, and the step of transmitting light signals includes transmitting light signals from the light source of the first transducer into the subject's tissue and transmitting light signals from the light source of the second transducer into the subject's tissue; and wherein the step of sensing the light signals includes sensing the light signals from the light source of the first transducer using the first and second light detectors of the first transducer, and sensing the light signals from the light source of the second transducer using the first and second light detectors of the second transducer.
 9. An apparatus for non-invasively determining an absolute non-pulsatile blood oxygen saturation level within a subject's tissue, comprising: a sensor having at least one transducer, the transducer having at least one light source, a first light detector spaced apart from the light source by a first distance, and a second light detector spaced apart from the light source by a second distance, wherein the first distance is less than the second distance, and a processor in communication with the transducer; wherein the transducer is operable to transmit light signals from the light source into the subject's tissue, wherein the transmitted light signals include a plurality of wavelengths, and is operable to sense the light signals using the first light detector and the second light detector, and communicate information representative of the sensed light signals to the processor; wherein the processor is adapted to determine an attenuation of the transmitted light signals for each of the plurality of wavelengths using the information representative of the sensed light signals, and is adapted to determine the absolute non-pulsatile blood oxygen saturation level within the subject's tissue, which saturation level determination includes determining a difference in attenuation between the plurality of wavelengths.
 10. The apparatus of claim 9, wherein the processor is adapted to determine one or both of an absolute non-pulsatile oxyhemoglobin concentration value and an absolute non-pulsatile deoxyhemoglobin concentration value.
 11. The apparatus of claim 9, further comprising a pulse oximeter operable to determine an arterial oxygen saturation of the subject.
 12. The apparatus of claim 11, wherein the processor is adapted to determine a venous oxygen saturation value within the subject's tissue using the arterial oxygen saturation determined using the pulse oximeter. 